Polypropylenes have been used widely as thermoplastic molding materials with high rigidity, heat resistance, transparency and the like. Because the polypropylenes are nonpolar materials, they show poor adhesion to polar materials such as ethylene/vinyl alcohol copolymers. To improve adhesion, it is generally known that the polypropylenes are modified with unsaturated carboxylic acids or derivatives thereof. Further, the polypropylenes have low flexibility. Therefore, the use of the polypropylenes as adhesives generally involves addition of soft rubber components. Adding soft rubber components to the polypropylenes results in polypropylene adhesives improved in adhesion (Patent Documents 1 and 2). However, such adhesives as disclosed in Patent Documents 1 and 2 cannot achieve high adhesion in multilayer structures produced by techniques such as high-speed cast film processing, stretching and extrusion coating. Accordingly, improvements in adhesion have been desired. Furthermore, the soft rubber components as described in Patent Documents 1 and 2 can cause blushing in secondary processing such as deep drawing, and therefore improved blushing resistance has also been desired.    Patent Document 1: JP-A-H09-111069    Patent Document 2: JP-A-H04-300933